Mathematical model for determining the volume of birch bark at woodworking enterprises when organizing the production of composite materials

In Russia, wood processing enterprises produce about 5 million m3 of birch bark every year, which is practically unused and is mostly burned. It has been established that a promising area for processing birch bark is the production of multifunctional composite materials, including bioplastics made from its components, such as birch bark. Despite the existing prerequisites for this development through various research and development projects, this area has not been widely pursued, primarily due to the lack of an accurate tool for assessing and predicting the quantity and characteristics of birch bark. For the first time, the generalized results of studies of the parameters of the downy birch bark are published based on the analysis of 482 samples from 16 model trunks of various diameters, as well as a multilayer mathematical model (birch bark-trunk) developed on their basis, which allows for the most accurate estimation of birch bark volumes and prediction of its reserves at woodworking enterprises. In addition, an analysis was conducted to determine the change in bark and birch bark thickness along the trunk length, as well as their volumes, depending on the diameter. The analysis showed that the highest thickness of birch bark and bark was observed in the base of the trunk, at 5.75 mm and 13.6 mm, respectively, while the lowest thickness was observed in the top of the trunk, at 0.62 mm and 3.25 mm, respectively. All of the model trunks that were studied showed a pattern in which the thickness of the birch bark increases with increasing diameter, and decreases along the length of the trunk from the base to the top. It has been established that the volume of birch bark and bark, depending on the diameter along the length of the trunk, does not correspond to the patterns established with the variability of their thickness: the proportion of birch bark and bark from the volume of wood in the lumpy part is 1.54...4.31% and 6.5...12.4%, respectively, in the middle part at a length of 7 to 15 meters decreases up to 0.85...1.45% and 3.9...7.1%, respectively, and in the upper quarter of the trunk there is a slight increase to values of 1.05...1.72% and 4.2...6.7%, respectively. At the same time, the share of birch bark in the volume of the fluffy birch trunk is 2.56…3.84%, and the share of the bark is 8.78…12.1%. These indicators depend on the parameters of the tree trunk, such as diameter and length, and, accordingly, on the age of the tree. The basis of the multilayer mathematical model (birch bark-trunk) is a mathematical description of the tree trunk using cubic spline functions defined in a parametric form, which allowed us to obtain multilayer 3-D models of each model tree trunk and estimate the volumes of each layer. The reliability of the results is 98.1%. Based on the developed software in the Python environment, we analyzed a number of large birch processing enterprises. The volume of birch bark from the annual program of enterprises ranges from 2.58% to 3.74%, and in absolute terms it reaches several thousand and even tens of thousands of tons. The research results led to the conclusion that, with a ready-made recycling program of more than 20000 m3, the production of multifunctional composite materials, including bio-plastics made from birch bark, will be effective. At the same time, it is necessary to improve and enhance the efficient production technology.